2.c is anyone good with exponential and logarithmic?
Accepted Solution
A:
Answer:After 48 months the value will increase by 10 percent of the initial value.Step-by-step explanation:Let's first find the rate of increase for each period which is 3 months here.According to the table at month [tex]x=0[/tex] value is [tex]2000[/tex]dollars and at month [tex]x=3[/tex] value is [tex]2012[/tex]dollars.∴[tex]2012=2000(1+\frac{r}{100} )^1[/tex]⇒[tex]1+\frac{r}{100} =\frac{2012}{2000}=1.006[/tex]⇒[tex]r=0.006*100[/tex]⇒[tex]r=0.6[/tex]%Now the question is to find how long it will take for the investment value to increase 10 percent.[tex]y=2000(1+0.006)^\frac{x}{3}[/tex] [tex]2000(1+0.1)=2000(1.006)^\frac{x}{3}[/tex]⇒[tex](1.006)^\frac{x}{3} =1.1[/tex]⇒[tex]\frac{x}{3}=\frac{log(1.1)}{log(1.006)}[/tex]⇒[tex]x=3(\frac{log(1.1)}{log(1.006)} )[/tex]⇒[tex]x=47.7979126....[/tex]∴at [tex]x=48[/tex] the value will slightly cross 10 percent increase.